Is it possible to make a 'forked path' neural network?
Keras Functional APIs can help you define complex models.

You can find the documentation here :
https://keras.io/getting-started/functional-api-guide/.

For example:

# prev_layer is the layer you want to be forked
fork1 = Dense(32, activation='relu')(prev_layer)
fork2 = Dense(32, activation='relu')(prev_layer)

# you do some operations on fork1 to get output1
# and on fork2 to get output2

model = Model(inputs=input_layer, outputs=[output1, output2])